ASTRONOMY. 69 



representation of smaller portions of the earth's 

 surface. 



a. In this construction, a straight line is drawn for 

 the meridian of the middle of the map, on which 

 are marked off equal distances, to denote degrees 

 of latitude. From a point in this line, as a centre, 

 and with a radius that is to the length of the de- 

 gree of latitude as the cotangent of the middle lati- 

 tude to an arch of i degree, an arch of a circle is 

 described, to represent the middle parallel of lati- 

 tude. From the same centre are described other 

 arches, through the different points marked off on 

 the meridian of the middle of the map, which re- 

 present the different parallels of latitude. On any 

 one of these parallels, equal distances are set off on 

 each side of the middle point, which are to the as- 

 sumed degree of latitude, as the cosine of the lati- 

 tude of that parallel to the radius. The degrees 

 of longitude are thus marked on each parallel, and 

 the curves which pass through the corresponding 

 points in the different parallels are meridians. 

 These are curved more and more on retiring 

 from the middle of the map ; but unless the extent 

 is very great, they afford a very good representa- 

 tion of the convex surface. 



&. This construction has a very remarkable property, 

 viz. that the quadrilaterals in the map, included be- 

 tween the meridians and parallels of latitude, have 

 the same ratio to one another nearly, with the qua- 

 drilaterals which they represent on the surface of 



the 



